The present invention relates generally to communication systems and, in particular, to joint detection of a coded signal in a CDMA system.
FIG. 1 depicts a discrete time baseband model 100 of a known CDMA system that supports K block transmission users. These users have simultaneous access to the same physical, frequency-defined channel and transmit data block by block, each block having N symbols. Each user, 1 through K, has a sequence of information bits, d(1) through d(K), to be transmitted. Each user""s sequence is first turbo encoded and mapped to channel symbol sequences s(1) through s(K) respectively. These channel symbol sequences are then spread by their corresponding code C(1) through C(K), each of which has Q random chips, and passed through their corresponding channel, characterized by impulse responses h(1) through h(K) with W taps at chip level. For simplicity, it is assumed that this system uses BPSK modulation, so s(1) through s(K) are sequences of 1 and xe2x88x921, and the physical channel is an additive white Gaussian noise (AWGN) channel.
At the receive end, the received signal r can be expressed:                     r        =                                            ∑                              k                =                1                            K                        ⁢                          xe2x80x83                        ⁢                                          s                                  (                  k                  )                                            ⁢                                                C                                      (                    k                    )                                                  ⊗                                  h                                      (                    k                    )                                                                                +          n                                        =                  As          +          n                    
where r is a summation of K sequences and n represents channel noise, each of the length (NQ+Wxe2x88x921). A is a (NQ+Wxe2x88x921) by NK matrix consisting of:
a(k)=(a1(k), a2(k), . . . , aQ+Wxe2x88x921(k))=C(k) {circle around (x)}h(k)
and s is a composite symbol vector combining all symbols of the K users and arranged in the following order:
s=(s1(1),s1(2), . . . ,s1(K),s1(1),s2(2), . . . ,s2(K) ,s3(1), . . . ,sN(1), . . . ,sN(K))T
where T denotes the transposition operation. The received signal r is passed through a bank of matched filters, each one matches a(k). The output of the matched filter bank, y, is a minimum sufficient statistic of transmitted signals for all K users and can be expressed as:
y=AHr=AHAs+z=Rs+z
where y, s, and z are NK by 1 vectors, and R is an NK by NK block toeplitz matrix. By using Cholesky factorization, R can be written as:
R=LLH=LnDLnH
where L is a lower triangular matrix, Ln denotes a normalized L in which all elements of the diagonal are ones, and D represents a diagonal matrix.
Joint detection is known to be an optimal receiver for CDMA systems. One well-known joint detector is implemented using a zero-forcing block linear equalizer (ZF-BLE). Its output may be expressed as:
sZF-BLE=Rxe2x88x921y=Lxe2x88x92HLxe2x88x921y=Lnxe2x88x92HDxe2x88x92xc2xdLxe2x88x921y
In practice, inversion of lower and upper triangular matrices can be achieved by forward and backward substitution. Therefore, by using Cholesky factorization, no actual matrix inversion is needed for joint detection. Another well-known joint detection technique, zero-forcing block decision feedback equalization (ZF-BDFE), is derived from ZF-BLE by using quantized previous samples, according to the symbol alphabet, in the backward substitution corresponding to the operation of Lnxe2x88x92H.
With regard to performance, ZF-BLE joint detection suffers from noise enhancement and thus performs very poorly in bad channel conditions where frequency response has a deep notch. ZF-BDFE joint detection does not have this drawback and therefore usually outperforms ZF-BLE joint detection. However, since the hard decision in conventional ZF-BDFE joint detection is generated by a simple slicer, the performance of ZF-BDFE joint detection will also degrade if the received signal-to-noise-ratio (SNR) is low. Unfortunately, turbo encoded signaling, which will be used in 3rd generation (3G) mobile systems, exhibits a low SNR. The improved joint detector disclosed in the co-pending application xe2x80x9cMETHOD AND APPARATUS FOR JOINT DETECTION OF A CODED SIGNAL IN A CDMA SYSTEMxe2x80x9d, Ser. No. 09/798,305, filed on Mar. 2, 2001, successfully addresses these deficiencies and provides at least a 1 dB improvement over these conventional joint detectors.
However, the improved joint detector achieves these performance improvements at the cost of computational complexity. For example, for turbo decoding that requires eight iterations, the improved joint detector requires approximately 4 times the computation of the conventional joint detectors. In practice, devices with greater computational requirements cost more to manufacture and have greater energy needs than devices requiring less computation. Thus, a method and apparatus for joint detection that achieves the benefits of the improved joint detector without the increased computational requirements is needed.